1. Maths for parents
Learning Legendz
Anne-Louise Warren

2. What we will cover
What do children need to know in order to be able to master calculation methods?
What methods will they learn?
how can you help at home?
fun activities for home
websites
Anne-Louise Warren

3. mental skills needed for written calculations
recall of many key facts
number bonds to ten
complements/bonds to 20, 100, 1000
adding +1 and +10, - 1, -10
adding/subtracting multiples of ten
multiplication facts up to 12 x12 and corresponding division facts
partitioning
Anne-Louise Warren

4. Addition The empty number line
The empty number line helps to record the steps on the way to calculating the total. The steps often bridge through a multiple of 10.
8 + 7 = 15
= or:
Partitioning
The next stage is to record mental methods using partitioning. Partitioning both numbers into tens and ones mirrors the column method where ones are placed under ones and tens under tens. This also links to mental methods.
Eg: = = = or = = = 123
Partitioned numbers are then written under one another:
Anne-Louise Warren

5. Formal addition Column method
In this method, recording is reduced further. Carry digits are recorded below the line, using the words 'carry 10' or 'carry 100', not 'carry 1'.
Later, extend to adding three two-digit numbers, two three-digit numbers, numbers with different numbers of digits and decimals.
Anne-Louise Warren

6. SUBTRACTION The empty number line Anne-Louise Warren
The empty number line helps to record the steps in mental subtraction. There are several ways to do this:
Counting Back - a calculation like can be recorded by counting back 27 from 74 to reach 47. or
Counting Up - the steps can also be recorded by counting up from the smaller number to find the difference
Anne-Louise Warren

7. SUBTRACTION 57 -25 57-20= 37, 37 -5 -32 Partitioning
Subtraction can be recorded using partitioning to write equivalent calculations that are easier to carry out mentally
57 -25
57-20= 37,
                           
        
                                       
Expanded column method
The partitioning stage should be followed by the expanded column method, where tens and units are placed under each other. This is where the concept of ‘borrowing’ is introduced
Example:
                           
        
                                       
Anne-Louise Warren

8. SUBTRACTION Example: 741 - 367 Column method
     
Example:
                                       
Column method
The expanded method is eventually reduced to:
Anne-Louise Warren

9. Multiplication Anne-Louise Warren
Initially multiplication is introduced as ‘repeated addition’ using vocabulary such as ‘lots of’ or ‘groups of’ and real objects or pictures.
3 lots of 3 = 9 leading to 3 x 3
Mental multiplication using partitioning
This allows the tens and ones to be multiplied separately to form partial products. These are then added to find the total product. Either the tens or the ones can be multiplied first but it is more common to start with the tens. This can look like……
43 x 5
= 215
Anne-Louise Warren

10. MULtiplication The Grid Method Anne-Louise Warren
This links directly to the mental method. It is an alternative way of recording the same steps. It is better to place the number with the most digits in the left-hand column of the grid so that it is easier to add the partial products. For TU x TU, the partial products in each row are added, and then the two sums at the end of each row are added to find the total product
38 x x 27
Anne-Louise Warren

11. Multiplication Expanded short multiplication Anne-Louise Warren
The next step is to represent the method in a column format, but showing the working. Attention should be drawn to the links with the grid method above. Children should describe what they do by referring to the actual values of the digits in the columns. For example, the first step in 38 × 7 is ‘thirty multiplied by seven’, not ‘three times seven’, although the relationship 3 × 7 should be stressed. Most children should be able to use this expanded method for TU × U by the end of Year 4.
Anne-Louise Warren

12. multiplication Anne-Louise Warren Expanded short multiplication
The same steps can be used when introducing TU x TU.
Anne-Louise Warren

13. MULTIPLICATION Anne-Louise Warren Short multiplication
The expanded method is eventually reduced to the standard method for short multiplication. The recording is reduced further, with carry digits recorded below the line. If, after practice, children cannot use the compact method without making errors, they should return to the expanded format of stage 3.
The step here involves adding 210 and 50 mentally with only the 5 in the 50 recorded. This highlights the need for children to be able to add a multiple of 10 to a two-digit or three-digit number mentally before they reach this stage
Anne-Louise Warren

14. MULTIPLICATION Long multiplication Anne-Louise Warren
This is applied to TU x TU as follows.
The carry digits in the partial products of 56 × 20 = 120 and 56 × 7 = 392 are usually carried mentally.
The aim is for most children to use this long multiplication method for TU × TU during year 5
Anne-Louise Warren

15. division
Initially division is introduced as ‘sharing’ using real objects or pictures. Share 10 apples equally between 2 children which eventually becomes 10 ÷ 2 = 5
Mental division using partitioning
One way to work out TU ÷ U mentally is to partition TU into smaller multiples of the divisor, then divide each part separately.
84 ÷ 7 might be:
In this example, using knowledge of multiples, the 84 is partitioned into 70 (most children will be secure with a multiple of 10) plus 14

16. DIVISION
Mental division using partitioning
or……

17. DIVISION YOUR CHILD MAY REFER TO THIS AS BUS STOP
Short division of TU ÷ U
For 81 ÷ 3, the dividend of 81 is split into 60, the highest multiple of 3 that is also a multiple 10 and less than 81, to give 60 + 21.Each number is then divided by 3.
leading to
YOUR CHILD MAY REFER TO THIS AS BUS STOP

18. DIVISION 'Expanded' method for TU ÷ U and HTU ÷ U
This method, often referred to as 'chunking', is based on subtracting multiples of the divisor, or 'chunks'. It is useful for reminding children of the link between division and repeated subtraction. However, children need to recognise that chunking is inefficient if too many subtractions have to be carried out.

19. DIVISION Refining the 'Expanded' method for HTU ÷ U
Initially children subtract several chunks, but with practice they should look for the biggest multiples that they can find to subtract, to reduce the number of steps.
Once they understand and can apply the expanded method, children should try the standard method for short division. For most children this will be at the end of Year 5 or the beginning of Year 6

20. DIVISION Long division for HTU ÷ TU
The next step is to tackle HTU ÷ TU, which for most children will be in Year 6. The layout on the right, which links to chunking, is in essence the 'long division' method. Conventionally the 20, or 2 tens, and the 3 ones forming the answer are recorded above the line, as in the second recording.

21. ACTIVITIES AND IDEAS
RECALL OF FACTS WHEN OUT AND ABOUT (KEEP IT LIGHTHEARTED AND ACHIEVABLE)
WRITING OUT FACTS IN FUN COLOURS/IN SAND
HOW MANY FACTS CAN THEY RECALL/CALCULATIONS CAN THEY SOLVE IN 1MIN/2MIN…
BAKING- HOW MUCH MORE…? ESTIMATING, MEASURING, QUANTITIES
TELLING THE TIME- HOW LONG UNTIL WE GO OUT? WHAT TIME DOES DINNER NEED TO COME OUT? WHAT DAY IS IT TODAY? TOMORROW? HOW MANY DAYS THIS MONTH?
USING THINGS YOU HAVE IN THE HOUSE
KEEP IT FUN AND SNAPPY, SHARE IN THE LOVE OF MATHS TOGETHER

22. USEFUL WEBSITES AND RESOURCES

23. Division

24. useful resources and ideas for home